91影视

Given : A nebula contains gas with : $100\mathrm{atoms}/c{m}^3$.

Temperature : $7500K$

Heated by : Ultraviolet radiation

Theory used :
The number density is given by $\frac{N}{V}$

The ideal gas law is given by $PV=nRT$
Rewriting ideal gas law for $V\mathrm{in}\mathrm{the}\mathrm{form}:$localid="1648796492843" $V=\frac{nRT}{p}$
If we know the number of molecules $N$, we obtain the number of moles $n$by using Avogadro's number :

$$\begin{gathered} n=\frac{N}{N_A} \\ 鈬�n=n{N}_A \end{gathered}$$

Now substitute the expressions for $N\mathrm{and}V$into number density formula to get the form of the number density $Numberdensity=\frac{N_A蚁}{RT}$
We obtain the number density by $100/cm鲁=0.01x{10}^{-6}/m鲁$.

We solve the above equation for$p$ to get the pressure in Pascal.
Now we substitute the values for N鈧�, P, R and T into the equation to get the number density
$p=\frac{RT}{N_A}$
We substitute the values for$R,T,N_A$and the number density to obtain
$$\begin{gathered} p=\frac{(8.314J/molK)(7500K)}{(6.023x1025molecules/mol)}(100x10m鲁) \\ =1.035x{10}^{-11}Pa \end{gathered}$$
Convert the pressure from pascal to atm into the form

$$\begin{gathered} p=(1.035脳{10}^{-11}Pa)\frac{1atm}{1.013x{10}^{5}Pa} \\ =1.02X{10}^{-16}atm \end{gathered}$$